'Though' at the end of a phrase has same meaning as 'but' at the beginning of it.
'I have a cold and I can't go tomorrow, but I will be fine to go next week.' =
'I have a cold and I can't go tomorrow. I will be fine to go next week, though.'
There is no need to have both 'but' and 'though' in the same sentence, as they both serve the same purpose. If you have both, 'though' simply reinforces the 'but'.
It's not necessarily a negative - it's just a contrast between tomorrow and next week.